The disclosed subject matter relates generally to wireless communications and, more particularly, to orthogonal frequency division multiple access (OFDMA) subband and power allocation.
Orthogonal frequency division multiplexing (OFDM) has developed into a popular scheme for wideband digital communication, whether wireless or over copper wires, and can be used in applications such as digital television and audio broadcasting, wireless networking and broadband internet access, as well as other digital communications applications. For multiuser communications, OFDM can be employed by dividing the total bandwidth into traffic channels or a subset of OFDM subcarriers so that multiple access can be accommodated in an orthogonal frequency division multiple access (OFDMA) schemes.
Conventional cross-layer optimization of power and subband allocation in OFDMA systems typically focus on optimizing physical layer performance, and thus, power and subband allocation solutions derived are functions of the channel state information (CSI) only. On the other hand, real life applications are delay-sensitive and it is critical to consider the bursty arrivals and delay performance in addition to the conventional physical layer performance (such as sum-rate or proportional fair) in OFDMA cross-layer design.
However, a combined framework that takes into account both queuing delay and physical layer performance is not trivial as it can be understood to involve both queuing theory (e.g., to model queue dynamics) and information theory (e.g., to model physical layer dynamics). For example, one such combined approach converts a delay constraint into an average rate constraint using tail probability at large delay regime and solves the optimization problem using information theoretical formulation based on the rate constraint. While this can allow a potentially simple solution, the derived control policy will be a function of the CSI only, which can be expected to have limited applicability to large delay regimes where the probability of buffer empty is small.
Accordingly, delay-optimal control actions should generally be a function of both the CSI and queue state information (QSI). In other approaches, a Longest Queue Highest Possible Rate (LQHPR) policy can be shown to be delay-optimal for multi-access fading channels, in limited theoretical contexts. For example, such solutions utilizing stochastic majorization theory can require symmetry among the users, which can be difficult or impractical to extend to other situations. In yet other approaches that focus on the queue stability region of various wireless systems using Lyapunov drift, the solutions can be limited to systems involving large delay.
While conventional solutions address different aspects of the delay sensitive resource allocation problem, there are still a number of first order issues to be addressed to obtain decentralized resource optimization for delay-optimal uplink OFDMA systems. For instance, while a more general approach can be to model the problem as a Markov Decision Problem (MDP), a primary difficulty in determining the optimal policy using the MDP approach is the huge state space involved. For instance, the state space is exponentially large in the number of users. As an example, for a system with 4 users, 6 independent subbands, a buffer size of 50 per user and 4 channel states, the system state space can contain an unmanageable number of 44×6×(50+1)4 states (e.g., due to the exponential growth of state space, etc).
In addition, conventional solutions are typically centralized in which processing is done at the base station (BS) requiring global knowledge of CSI and QSI from K users. However, in the uplink direction, the QSI is typically only available locally at each of the K users. Hence, centralized solution at the BS could require all the K users to deliver their QSI to the BS, which can consume enormous signaling overhead, and could require the BS to broadcast the allocation results for the resource allocations at the mobile side in the uplink system. In addition, such centralized solutions could lead to an exponential computational complexity of the BS.
Moreover, while a number of conventional solutions for decentralized OFDMA control use deterministic game or primal-dual decomposition theory for solving deterministic network utility maximization, such derived distributed algorithms are iterative in nature where all nodes are expected to exchange some messages explicitly in solving the master problem. However, in such conventional solutions, CSI is typically assumed to be quasi-static during the iterative updates with message passing. When considering delay-optimization, the problem may not be static or quasi-static but can be expected to be stochastic in nature. As a result, delay-optimization is quite challenging, because the game, as it were, is played repeatedly and the actions as well as the payoffs are defined over ergodic realizations of the system states (e.g., CSI, QSI). Thus, during iterative updates, the system state will be expected to be not quasi-static, and as a result, convergence of a stochastic iterative solution is not assured.
The above-described deficiencies are merely intended to provide an overview of some of the problems encountered in providing distributed delay-optimal power and subband allocation design for uplink OFDMA systems, and are not intended to be exhaustive. Other problems with conventional systems and corresponding benefits of the various non-limiting embodiments described herein may become further apparent upon review of the following description.
A simplified summary is provided herein to help enable a basic or general understanding of various aspects of exemplary, non-limiting embodiments that follow in the more detailed description and the accompanying drawings. This summary is not intended, however, as an extensive or exhaustive overview. The sole purpose of this summary is to present some concepts related to the various exemplary non-limiting embodiments of the disclosed subject matter in a simplified form as a prelude to the more detailed description that follows.
In consideration of the above-described deficiencies of the state of the art, the disclosed subject matter provides apparatuses, related systems, and methods associated with subband and power allocation.
According to non-limiting aspects, a network entity, such as a base station (BS), a resource allocation controller, or the like, can determine a subband allocation policy, and so on, based in part on both channel state information (CSI) and queue state information (QSI) as further described herein.
Thus, in various non-limiting implementations, the disclosed subject matter provides systems for wireless communication resource allocation configured to perform a per-stage subband auction, to facilitate subband and power allocation based in part on joint channel state information and joint queue state information. In other non-limiting implementations, methods are provided that facilitate resource allocation (e.g., subband and power allocation) in a wireless communication system by generating a resource allocation policy based on bids for resource allocation and a per-stage subband auction mechanism as further described herein. Further exemplary implementations are directed to a resource allocation controller configured to perform various non-limiting aspects of the disclosed subject matter. Additionally, various modifications are provided, which achieve a wide range of performance and computational overhead trade-offs according to system design considerations.
In various non-limiting implementations a distributed delay-optimal power and subband allocation design for uplink OFDMA system, which can be cast into an infinite-horizon average-cost CMDP is described herein. To address the distributed requirement and the issue of exponential memory requirement and computational complexity, various non-limiting implementations can employ a per-user online learning with per-stage auction, which can employ local QSI and local CSI. It is demonstrated that under the per-stage auction as described herein, the distributed online learning solution converges with probability 1. As a non-limiting illustration, non-limiting implementations of the described learning algorithm can be applied to an application example with exponential packet size distribution. According to various non-limiting aspects, delay-optimal power control as described herein can have the multi-level water-filling structure, and non-limiting implementations of the described learning algorithm can converge to the global optimal solution for sufficiently large number of users. Numerical simulation results described herein demonstrate significant delay performance gain over various comparative baselines.
These and other embodiments are described in more detail below.
The disclosed techniques and related systems and methods are further described with reference to the accompanying drawings in which:
Simplified overviews are provided in the present section to help enable a basic or general understanding of various aspects of exemplary, non-limiting embodiments that follow in the more detailed description and the accompanying drawings. This overview section is not intended, however, to be considered extensive or exhaustive. Instead, the sole purpose of the following embodiment overviews is to present some concepts related to some exemplary non-limiting embodiments of the disclosed subject matter in a simplified form as a prelude to the more detailed description of these and various other embodiments of the disclosed subject matter that follow.
It is understood that various modifications may be made by one skilled in the relevant art without departing from the scope of the disclosed subject matter. Accordingly, it is the intent to include within the scope of the disclosed subject matter those modifications, substitutions, and variations as may come to those skilled in the art based on the teachings herein.
As used in this application, the terms “component,” “module,” “system”, or the like can refer to a computer-related entity, either hardware, a combination of hardware and software, software, or software in execution. For example, a component may be, but is not limited to being, a process running on a processor, a processor, an object, an executable, a thread of execution, a program, and/or a computer. By way of illustration, both an application running on a controller and the controller can be a component. One or more components may reside within a process and/or thread of execution and a component may be localized on one computer and/or distributed between two or more computers. Also the terms “user,” “mobile user,” “mobile device,” “mobile station,” and so on are used interchangeably to describe technological functionality (e.g., device, components, or subcomponents thereof, combinations, and so on etc.) configured to at least receive and transmit electronic signals and information according to various aspects of the disclosed subject matter.
In various non-limiting implementations, the disclosed subject matter provides distributed queue-aware power and subband allocation designs for delay-optimal OFDMA uplink systems. For example, the disclosed subject matter is described in the context of an OFDMA uplink system with one base station (BS), K users, and NF independent subbands, as further described below regarding
As a non-limiting illustration, a distributed stochastic learning framework is described herein for an application example with exponential packet size distribution. Thus, in various non-limiting implementations, delay-optimal power control can exhibit a multi-level water-filling structure where CSI can determine instantaneous power allocation and QSI can determine the water level. In addition, for sufficiently large number of users, it can be shown that the disclosed algorithms converge to a global optimal solution and can have linear signaling overhead and computational complexity (KN), which is desirable from an implementation perspective.
To address the distributed requirement and the issue of exponential memory requirement and computational complexity, a distributed online stochastic learning algorithm is described herein, which can employ knowledge of the local QSI and the local CSI at each of the K mobiles and can be utilized to determine the resource control actions using a per-stage auction. For example, in various non-limiting implementations, subband allocation Q-factor can be approximated by the sum of the per-user subband allocation Q-factor and a distributed online stochastic learning algorithm can be employed to estimate the per-user Q-factor and the LMs simultaneously and determine the control actions using an auction mechanism. Under the disclosed auction mechanism, the distributed online learning converges almost surely (with probability 1), as further described herein.
As mentioned, in an exemplary system model 100 including an OFDMA physical layer model as well as an underlying queuing model, there can be one BS 102 and K mobile users 106 (e.g., each with one uplink queue 108) in the OFDMA uplink system 100 with L subcarriers over a frequency selective fading channel with NF independent multipaths or subbands 104 as illustrated in
Accordingly, describing an exemplary OFDMA physical layer model, sk,nε{0,1} can denote the subband allocation for the k-th user 122 at the n-th subband 124, and the received signal from the k-th user 122 at the n-th subband 124 of the base station 102 can be given by Yk,nr=Sk,n(Hk,ntXk,nt+Zk,n), where Xk,nt can denote the transmitted symbol, Hk,n and Zk,n(˜(0,1)) are random fading and channel noise of the k-th user 122 at the n-th subband 124, respectively. The data rate of user k 122 can be expressed as:
for some constant ξ. Note that the data rate expression in Eqn. 1 can be used to model both the uncoded and coded systems. For uncoded system using Multi-Level Quadrature Amplitude Modulation (MQAM) constellation, the bit error rate (BER) of the n-th subband 124 and the k-th user 122 can be given by
where Γk,n can denote received signal-to-noise ratio (SNR) of the k-th user 122 at the n-th subband 124, and hence, for a target BER ε,
On the other hand, for system with powerful error correction codes such as low-density parity-check (LDPC) with reasonably large block length (e.g., 8 Kilobyte (Kbyte)) and target packet error rate (PER) of 0.1 percent (%), the maximum achievable data rate can be given by instantaneous mutual information (to within 0.5 decibel (dB) SNR). In that case, ξ=1. It is noted that for notation simplicity, derived results as described herein are based on ξ=1, which results can be easily extended to other cases.
The following describes exemplary source model, queue dynamics and control policy suitable for illustration of various non-limiting aspects of the disclosed subject matter. For instance, in various examples, the time dimension can be partitioned into scheduling slots indexed by t with slot duration τ.
Assumption 1: Joint CSI 112 of an exemplary system 100 can be denoted by H(t)={|Hk,n(t)|∀k,n}, where |Hk,n(t)| can denote a discrete random variable (r.v.) distributed according to Pr[|H|]. The CSI 112 can be assumed quasi-static within a scheduling slot and independently and identically distributed (i.i.d.) between scheduling slots. It is noted that while the quasi-static assumption can be a realistic assumption for pedestrian mobility users where the channel coherence time is around 50 milliseconds (ms), typical frame duration is less than 5 ms in next generation wireless systems such as WiMAX™. On the other hand, it can be assumed the CSI is i.i.d. between slots in order to capture first order insights. Similar solution frameworks can also be extended to deal with correlated fading.
In a further non-limiting aspect, A(t)=(A1(t), . . . , AK(t)) can denote the random new arrivals (number of bits) at the end of the t-th scheduling slot.
Assumption 2: The arrival process Ak(t) can be assumed i.i.d. over scheduling slots according to a general distribution Pr(Ak) with average arrival rate [Ak]=/λk.
Let Q(t)=(Q1(t), . . . , QK(t)) denote the joint QSI 114 of the K-user OFDMA system 100, where Q, (t) 126 can denote the number of bits in the k-th queue at the beginning of the t-th slot. NQ can denote the maximum buffer size (number of bits). Thus, the cardinality of the joint QSI 114 can be IQ=(NQ+1)K, which can be expected to grow exponentially with K. Let NH denote the cardinality of |Hk,n|(∀k,n). Hence, the cardinality of the global CSI can be given by IH=NHN
Q
k(t+1)=min{[Qk(t)−Rk(t)τ]++Ak(t),NQ}, ∀kε{1,K} (2)
where x+max {x,0} and τ can denote the duration of a scheduling slot.
For notation convenience, χ(t)=(H(t),Q(t)) can denote the global system state at the t-th slot. Therefore, the cardinality of the state space of χ is Iχ=IH×IQ=(NHN
Definition 1: Stationary Power Control and Subband Allocation Policy: A stationary transmit power and subband allocation policy Ω=(Ωp,Ωs) can be a mapping from the system state χ to the power and subband allocation actions. According to a non-limiting aspect, a policy Ω can be called feasible if the associated actions satisfy an average total transmit power constraint and a subband assignment constraint. Specifically, a policy Ω can be called feasible if Ωp(χ)=p={pk,n≧0:∀k,n} 118 and Ωs(χ)=s={sk,nε{0,1}:∀k,n} 120 satisfy
In further non-limiting implementations, Ω can also satisfy an average packet drop rate constraint for each queue as follows:
Pr[Q
k
=N
Q
]≦P
k
d
,∀kε{1,K} (5)
From Eqn. 1, the vector queue dynamics can be seen to be Markovian with the transition probability given by
Note that the K queues 108 can be coupled via the control policy Ω and the constraint in Eqn. 4.
From Assumption 1, the induced random process χ(t)=(H(t),Q(t)) can be expected to be Markovian with the following transition probability:
where Pr[Q(t+1)|χ(t),Ω(χ(t))] can be given by Eqn. 6. Given a unichain policy Ω, the induced Markov chain {χ(t)} can be ergodic and there can exist a unique steady state distribution πχ where
it is noted that, although the QSI Q(t+1) 112 and CSI H(t) 114 can be correlated via the control action Ω(χ(t)), due to the i.i.d. assumption of CSI in Assumption 1, H(t+1) can be expected to be independent of χ(t). Note further that H(t) being i.i.d. is a special case of Markovian model. Thus, Eqn. 7 can be expected to hold under the H(t) i.i.d. assumption in Assumption 1. Accordingly, the average utility of the k-th user under a unichain policy Ω can be given by:
where f(Qk) denotes a monotonic increasing function of Qk and π
can denote the average delay of the k-th user 122. Another interesting example, the queue outage probability,
Similarly, the average transmit power constraint in Eqn. 3 and the packet drop constraint in Eqn. 5 can be written as
According to various non-limiting implementations, the delay-optimal problem can be formulated as an infinite horizon average cost constrained Markov Decision Problem (CMDP). As a non-limiting example, an MDP can be characterized by a tuple of four objects (e.g., the state space, the action space, the transition probability kernel, and the per-stage cost function). In the delay-optimization problem, these four objects can be associated as follows:
State Space: The state space for the MDP can be given by {χ1, . . . , χI
Action Space: The action space of the MDP can be given by {Ω(χ1), . . . , Ω(χI
Transition Kernel: The transition kernel of the MDP Pr[χj|χi,Ω(χi)] can be given by Eqn. 7.
Per-stage Reward: The per-stage cost function of the MDP can be given by
As a result, in various non-limiting implementations, the delay-optimal control problem can be formulated as a CMDP, which is summarized below.
Problem 1: Delay-Optimal Constrained MDP: For some positive constants β=(β1, . . . , βK), the delay-optimal problem is formulated as
subject to the power and packet drop rate constraints in Eqns. 9 and 10. It is noted that the positive weighting factors β in Eqn. 11 can indicate the relative importance of buffer delay among the K data streams and for each given β, the solution to Eqn. 11 can corresponds to a point on the Pareto optimal delay tradeoff boundary of a multi-objective optimization problem.
In a Lagrangian approach to the CMDP, for any LMs
where γ=(γ1, . . . , γK) with γk=
and
Thus, the corresponding unconstrained MDP for a particular LM γ can be given by
G(γ)=minΩLβ(Ω,γ) (12)
where G(γ) gives the Lagrange dual function. The dual problem of the primal problem in Problem 1 can be given by G(γ). The general solution to the unconstrained MDP in Eqn. 12 is summarized in the following lemma
Lemma 1, Bellman equation and subband allocation Q-factor, for a given γ, the optimizing policy for the unconstrained MDP in Eqn. 11 can be obtained by solving Bellman equation (associated with the MDP in Eqn. 11 with respect to (θ,{(χ,s)}) as below:
where θ=L*β(γ)=minΩLβ(Ω,γ) denotes the optimal average cost per stage and {(χ,s)} denotes the subband allocation Q-factor. The optimal control policy can be given by Ω*=(Ωp*,Ωs*) with Ωp*(χi) attaining the minimum of the right hand side (R.H.S.) of Eqn. 13 and Ωs*(χi)=arg mins(χi,s) for any χi. Because the policy space considered consists of only unichain policies, the associated Markov chain {χ(t)} can be expected to be irreducible and there exists a recurrent state. It is noted that for sufficiently large total transmit power {P1, . . . , PK} so that the optimization problem in Eqn. 11 is feasible, and the state χ=(H,Q) (∀H and Q=(0, . . . , 0)) is recurrent. Thus, the solution to Eqn. 14 can be seen to be unique up to an additive constant.
As proof of Lemma 1, for a given γ, the optimizing policy for the unconstrained MDP in Eqn. 12 can be obtained by solving the Bellman Equation in Eqn. 13 with respect to (θ,{V(χ)}) as below:
where χ(χi)=(p,s) can denote the power control and subband allocation actions taken in state χi,
can denote the optimal average cost per stage, {V(χ)} can denote the potential function of the MDP.
Because Ω(χi)=(χs(χi),Ωp(χi)), the subband allocation Q-factor of state χi under subband allocation action s can be defined
as
Thus, V(χ)=mins(χ,s) (∀χ) and {(χ,s)} are shown satisfy the Bellman equation in Eqn. 13.
Using standard optimization theory, the problem in Eqn. 12 has an optimal solution for a particular choice of the LM γ=γ*, where γ* can be chosen to satisfy the average power constraint in Eqn. 9 and the packet drop constraint in Eqn. 10. Moreover, it can be shown that the following saddle point condition holds:
L(Ω*,γ)≦L(Ω*,γ*)≦L(Ω,γ) (15)
In other words, (Ω*,γ*) can be expected to be a saddle point of the Lagrangian, then Ω* can be the primal optimal (e.g., solving Problem 1), γ* is the dual optimal (solving the dual problem), and the duality gap can be expected to be zero. Accordingly, in various non-limiting implementations, by solving the dual problem, the primal optimal Ω* can be obtained. It is noted that the optimal control actions can be functions of the subband allocation Q-factor {(χ,s)} and the LMs, according to a non-limiting aspect. Unfortunately, for any given LMs, determining the subband allocation Q-factor involves solving the Bellman equation in Eqn. 13, which is a fixed-point problem over the functional space with exponential complexity. In other words, it is a system of KN
To arrive at a general decentralized solution via localized stochastic learning and auction, according to various non-limiting aspects, key steps in obtaining the optimal control policies from the R.H.S. of the Bellman equation in Eqn. 13 rely on the knowledge of the subband allocation Q-factor {(χ,s)} and the LMs {
is described herein according to further non-limiting aspects. Based on the approximate Q-factor, various embodiments of the disclosed subject matter can employ a per-stage decentralized control policy using a per-stage auction. In addition, further embodiments of the disclosed subject matter can employ a localized online stochastic learning algorithm (performed locally at each MS k 122) to determine the per-user Q-factor {k(χk,sk)} 126 as well as the two local LMs γk=(
For the linear approximation on the subband allocation Q-Factor and distributed power control, according to various aspects, the per-user system state, channel state, subband allocation actions, and power control actions can be denoted as χk=(Qk,Hk), Hk={|Hk,n|:∀n}, sk={sk,n:∀n} and pk={pk,n:∀n}, respectively. To reduce the size of the state space and to decentralize the resource allocation, (χ,s) can be approximated, as described above, by the sum of per-user subband allocation Q-factor k(χk,sk), e.g.,
where k(χk,sk) satisfies the following per-user subband allocation Q-factor fixed-point equation for each MS k:
where
and Wk(χk)=k(χk,{sk,n=1[|Hk,n|≧HK-1*]})|χk] (HK-1* denotes the largest order statistic of the (K−1) i.i.d. random variables with the same distribution as |Hk,n|), and Iχk=NHN
According to further non-limiting aspects, for a per-stage subband auction, the subband allocation control can be obtained by minimizing the original subband allocation Q-factor in Eqn. 13 over subband allocation actions. Using the approximate Q-factor, the subband allocation control can be given by
This can be obtained via a per-stage subband auction with K bidders or mobiles stations (MSs) and one auctioneer or base station (BS) based on the observed realization of the system state at each MS χk. The Per-Stage Subband Auction among K MSs can be implemented, according to various aspects, as follows.
For example, for bidding, based on the local observation χk, each user k 122 can submit a bid {k(χk,sk):∀sk}. In a further non-limiting example, for subband allocation, the BS 102 can assign one or more subbands to achieve the maximum sum bids, e.g.,
and can then broadcast the allocation results s*={sk*:∀k} to the K users 104. For power allocation, based on the subband allocation result sk*, each user k 122 can determine the transmit power, which can minimize the R.H.S. of Eqn. 17, e.g.,
It should be noted that, according to non-limiting aspects, optimal subband and power allocation under Q-factor approximation employing proposed per-stage subband auction, the subband allocation actions can minimize
and the power allocation actions at each MS or user k 122 can minimize the R.H.S. of the per-user subband allocation Q-factor fixed point equation in Eqn. 17. Therefore, the per-stage subband auction can achieve the solution of the Bellman equation in Eqn. 13 under the linear Q-factor approximation in Eqn. 16.
It is further noted regarding computational complexity and memory requirement reduction at the BS 102 that, with the per-stage subband auction mechanism, the BS 102 does not need to store the per-user subband allocation Q-factor {k(χk,sk)} (∀k) and 2K LMs for all the MSs users 104, which can greatly reduce the memory requirement at the BS 102, according to various non-limiting aspects. As a further non-limiting advantage, on the other hand, the BS 102 does not need to perform power allocation for each MS on each subband pk,n(∀k,n), which can significantly reduce the computational complexity at the BS 102.
In still further non-limiting aspects, according to an online per-user primal-dual learning algorithm via a stochastic approximation, because the derived power and subband allocation policies represent functions of the per-user subband allocation Q-factor and LMs, an online localized learning algorithm can estimate {k(χk,sk)} and LMs γk at each MS k 122. For notation convenience, the per-user state-action combination can be denoted as φ(χk,sk) (∀k). Let i and j (1≦i,j≦Iφ) be the dummy indices enumerating all the per-user state-action combinations of each user with cardinality Iφ=2N
t+1
k(φi)=tk(φi)+εk
γ
t+1
k=Γ(γtk+εtγ(1[Qk(t)=NQ]−Pkd)) (22)
where
represents the number of updates of k(φi) till t, pk(t)={pk,n(t):∀n} denotes the power allocation actions given the per-stage auction, {tilde over (W)}tk(k)[Wtk(χk)|k] with Wtk(χk)=[tk[k,{sk,n=1[|Hk,n|≧HK-1*]})|χk],
Note that without loss of generality, the per-user subband allocation Q-factor can be initialized as zero, e.g., 0k(φr)=0∀k . According to various non-limiting implementations of the disclosed subject matter, the above distributed per-user potential learning algorithm requires knowledge on local QSI and local CSI only. It is further noted that, in comparison to the deterministic network utility maximization (NUM), in conventional iterative solutions for deterministic NUM, the iterative updates (with message exchange) are performed within the CSI coherence time and hence, this limits the number of iterations and the performance. For instance, because the iterations within a CSI coherence time involve explicit message passing, there is processing and signaling overhead per iteration that can limit the total number of iterations within a CSI coherence time. However, in the online algorithm of various non-limiting implementations, the updates can evolve in the same time scale as the CSI and QSI. Thus, it can be understood that the various embodiments of the disclosed subject matter can converge to a better solution because the number of iterations is no longer limited by the coherence time of CSI.
Moreover, regarding comparison to conventional reinforced learning, various aspects of the per-user online update algorithms provide advantages over conventional techniques. As a non-limiting example, conventional online learning techniques typically address unconstrained MDP only. In the case of CMDP, the LM can be determined offline by simulation. In contrast, according to various non-limiting embodiments of the disclosed subject matter, both the LM and the per-user Q-factor are updated simultaneously. In a further non-limiting example, conventional online learning techniques are typically designed for centralized solutions where the control actions are determined entirely from the potential or Q-factor update. However, according to various non-limiting embodiments of the disclosed subject matter, the control actions for user k 122 can be determined from {k(φ)} (∀k) via a per-stage auction. Moreover, during iterative updates, the per-user Q-factor, the LMs, and the control actions (e.g., power 118 and subband 120 allocation policies, etc.) can be changed dynamically and the existing convergence results (e.g., based on contraction mapping argument) may not be able to be applied directly to the distributed stochastic learning algorithm.
In the analysis of convergence of the online distributed learning algorithm, technical conditions for the almost-sure convergence of the online distributed learning algorithm can be established. For instance, for any LM γ (γk≧0), define a vector mapping Tk:R2×RI
where
Define
A
t−1
k
P
t
kεt−1v+(1−εt−1v)I,
B
t−1
k
P
t
kεt−1v+(1−εt−1v)I (24)
where Ptk denotes the Iφ×Iφ transition probability matrix with Pr[φj|φi,ptk(i)] as its (i,j)-element, ptk(i) denotes the power allocation for φi obtained by per-stage subband auction at the t-th iteration, and I denotes the Iφ×Iφ identity matrix.
Because there can be two different step size sequences {εtγ} and {εtq} and εtγ=o(εtq), the LM updates and the per-user Q-factor updates can be done simultaneously but over two different time scales. During the per-user Q-factor update (timescale I),
where e(t)=(εtγ)=o(εtq). Therefore, the LM can appear to be quasi-static during the per-user Q-factor update in Eqn. 20. Accordingly, the following lemma can be employed.
Lemma 2, convergence of per-user Q-factor learning over timescale I, assume for all the feasible policies Ω in the policy space, there exists a δm=(εmq)>0 and some positive integer m such that
[Amk . . . Alk]ir≧δm, Bmk . . . Blk]ir≧δm, 1≦i≦Iφ (25)
where [.]ir can denote the element of the i-th row with r-th column of the corresponding Iφ×Iφ matrix (r represents the column index in Ptk which contains the aggregate reference state φr). For step size sequence {εtq},{εtγ} satisfying the conditions in Eqn. 23,
almost surely (a.s.) for any initial per-user subband allocation Q-factor vector 0k and LM γ, where the converged per-user subband allocation Q-factor ∞k(γ) satisfies:
(Trk(γk,∞k(γ))−∞k(φr))e+∞k(γ)=Tk(γk,∞k(γ)) (26)
As proof of Lemma 2, because ∀k , each state-action pair φi can be updated comparably often, the only difference between the synchronous update and asynchronous update can be that the resultant ordinary differential equation (ODE) of the asynchronous update is a time-scaled version of the synchronous update. However, it does not affect the convergence behavior. Therefore, the convergence of related synchronous version for simplicity can be considered in the following.
Due to symmetry, the update for user k can be considered. It can be proved that the synchronous version of the per-user Q-factor update in Eqn. 20 can be equivalent to the per-user Q-factor update given by
t+1
k(φi)=tk(φi)+εtqYtk(γk,φi) 1≦i≦Iφ (27)
where Ytk(γk,φi)=gk(γk,φi,pk(t))+{tilde over (W)}tk(Qk(t+1))−(gk(γk,φr,pk(
Denote Ytk(γtk(γk,φ1), . . . , Ytk(γk,φI
denote the expectation and probability conditioned on the σ-algebra t, generated by {0,Yi,i<t}, e.g., t[.]=[.|t] and
Define Rtk(γk,φi)t[Ytk(γk,φi)]=Tik(γk,tk)−tk(φi)−(Trk(γk,tk)−tk(φr)) and δMtk(φi)Ttk(γk,φi)−t[Ytk(γk,φi)]. Thus, δMtk(φ1) is the martingale difference noise satisfying the property that t[δMtk(φi)]=0 and [δMtk(φi)δMt′k(φi)]=0 (∀t≠t′). For some j, define
Then, from Eqn. 27, it follows that
Since t [Mtk(φi)]=Mt−1k(φi), Mtk(φi) is a Martingale sequence. By martingale inequality, it follows that
By the property of martingale difference noise and the condition on the step size sequence, it follows
that
where
that
Thus, from Eqn. 28,
a.s. with the vector form
where Rlk=Tk(γk,lk)−lk−(Trk(γk,lk)−lk(φr))e and e=[1, . . . , 1]T denote the Iφ×1 unit vector.
Next, the convergence of the dynamic equation in Eqn. 29 can be established after the martingale noise is averaged out. Let gtk and Ptk denote the cost column vector and the transition probability matrix under the power allocation ptk, which attains the minimum of Tk of the t-Th iteration.
Denote ztk=Trk(γk,tk)−tk(φr). Then, it follows that
Since Rtk(γk,φr)=Trk(γk,tk)−tk(φr)−(Trk(γk,tk)−tk(φr))=0 ∀t, by Eqn. 25, it follows that
where φj>0. Since Rtk(γk,φr)=0 ∀t, it follows that maxi′Rtk(γk,φi′)≧0 and mini′Rtk(γk,φi′)≦0. Thus, ∀i , it follows
that
Therefore, as t→∞, Rtk→0, e.g., ∞k(γ) satisfies the equation in Eqn. 26. Similar to the potential function of Bellman equation, the solution to Eqn. 26 is unique only up an additive constant. Since lk(φr)=0k(φr) ∀t, it follows that have the convergence of the per-user subband allocation Q-factor
almost surely.
On the other hand, during the LM update (timescale II),
with probability one (w.p.1) as is shown elsewhere. Hence, during the LM updates in Eqn. 21 and Eqn. 22, the per-user subband allocation Q-factor update can be seen as almost equilibrated. The convergence of the LM can be summarized as follows in Lemma 3 and the proof thereof.
Lemma 3, convergence of the LM over timescale II, the iterates
where γ∞ satisfies the power and packet drop rate constraints in Eqn. 9 and Eqn. 10.
As proof of Lemma 3, due to the separation of time scale, the primal update of the Q-factor can be regarded as converged to ∞k(γt) with respect to the current LMs γt. Using standard stochastic approximation theorem, the dynamics of the LMs update equation in Eqns. 21 and 22 can be represented by the following ODE:
where Ω*(γ(t))=(Ωp*(γ(t)),Ωs*(γ(t))) is the converged control policies in Eqns. 19 and 18 with respect to the current LM γ(t), and Ω*(γ(t))[.] denotes the expectation with respect to the measure induced by Ω*(γ).
Since subband allocation policy can be discrete, it follows that Ωs*(γ)=Ωs*(γ+δγ). Hence, by chain rule, it follows that
it follows that
Therefore, we show that the ODE in Eqn. 30 can be expressed as γ(t)=∇G(γ(t)). As a result, the ODE in Eqn. 30 will converge to ∇G(γ)=0, which corresponds to Eqns. 9 and 10.
Based on the above lemmas, the convergence performance of the online per-user Q-factor and LM learning algorithm can be summarized in Theorem 1.
Theorem 1, convergence of online per-user learning algorithm, For the same conditions as in Lemma 2, (tk,γtk)→(∞k,γ∞k) a.s. ∀k , where ∞k(γ∞) and γ∞ satisfy
(Trk(γ∞k,∞k)−∞k(φr))e+∞k=Tk(γ∞k∞k) (31)
and γ∞ satisfies the power and packet drop rate constraints in Eqn. 9 and Eqn. 10.
Application to OFDMA Systems with Exponential Packet Size Distribution
According to further non-limiting aspects, various non-limiting aspects of the disclosed subject matter (e.g., stochastic learning algorithms, etc.) can be employed in uplink OFDMA systems 100 with exponential packet size distribution. To illustrate dynamics of system 100 state under exponential distributed packet size, let A(t)=(A1(t), . . . , AK(t)) and N(t)=(N1(t), . . . , NK(t)) denote random new packet arrivals and the packet sizes for the K users 104 at the t-th scheduling slot, respectively. Q(t)=(Q1(t), . . . , QK(t)) and NQ can denote the joint QSI (number of packets) 114 at the end of the t-th scheduling slot and the maximum buffer size (number of packets).
Assumption 3: The arrival process Ak(t) can be assumed to be i.i.d. over scheduling slots according to a general distribution Pr(Ak) with average arrival rate [Ak]=λk. In addition, the random packet size Nk(t) can be assumed to be i.i.d. over scheduling slots following an exponential distribution with mean packet size
Given a stationary policy, the conditional mean departure rate of packets of user k 122 at the t-th slot (conditioned on χ(t)) can be defined as μk(χ(t))=Rk(χ(t))/
Assumption 4: The slot duration τ can be assumed to be sufficiently small compared with the average packet service time, e.g., μk(χ(t))τ<<1.
It is noted that this assumption can be understood to be reasonable in practical systems. For instance, in the uplink (UL) WiMAX™ (with multiple UL users served simultaneously), the minimum resource block that could be allocated to a user in the UL is 8×16 symbols−12 pilot symbols=116 symbols. Even with 64 Quadrature Amplitude Modulation (QAM) and rate ½ coding, the number of payload bits it can carry is 116×3 bits=348 bits. As a result, when there are many UL users sharing the WiMAX™ access point (AP), there could be cases that the Moving Picture Experts Group (MPEG) standard MPEG-4 packet (around 10,000 bits) from an UL user cannot be delivered in one frame. In addition, the delay requirement of MPEG-4 is 500 milliseconds (ms) or more, while the frame duration of WiMAX™ is 5 ms. Thus, it is not necessary to serve one packet during one scheduling slot so that the scheduler has more flexibility in allocating resource. Therefore, in practical systems, an application level packet may have mean packet length spanning over many time slots (frames) as is typically assumed in conventional understanding.
Given the current system state χ(t) and the control action, and conditioned on the packet arrival A(t) at the end of the t-th slot, there can be a packet departure of the k-th user 122 at the (t+1)-th slot if the remaining service time of a packet is less than the current slot duration τ. By the memoryless property of the exponential distribution, the remaining packet length (also denoted as N(t)) at any slot t can also be exponentially distributed. Thus, the transition probability to Qk(t+1) at the (t+1)-th slot corresponding to a packet departure event can be given by:
where the last equality is due to Assumption 4. Note that, because Nk(t) can be exponentially distributed and memoryless, the probability in Eqn. 32 (conditioned on the current state χ(t) and the associated action Ω(χ(t))) independent of the previous states {χ(t−1), χ(t−2), . . . } can result. Note further that the probability for simultaneous departure of two or more packets from the same queue or different queues in a slot can be ((μk(χ(t))τ)2), which can be expected to be asymptotically negligible. Therefore, the vector queue dynamics can be expected to be Markovian with the transition probability given by
where ek can denote the standard basis vector with 1 for its k-th component and 0 for every other component.
In the following lemma, the per-user subband allocation Q-factor k(χk,sk) can be shown to be further decomposable into the sum of per-user per-subband Q-factor, which can further simplify the learning algorithm, according to a further non-limiting aspect of the disclosed subject matter.
Lemma 4, decomposition of per-user Q-factor, the per-user Q-factor k(χk,sk) (which can be defined by the fixed point equation in Eqn. 17) can be decomposed into the sum of the per-user per-subband Q-factor {qk(Q,|H|,s)}, e.g.,
where
{tilde over (w)}
k(Qk)=[qk(Qk,|Kk,n|,sk,n=1[|Hk,n|≧KK-1*])|Qk] (36)
δ{tilde over (w)}k(Qk)=[{tilde over (w)}k(Qk+Ak)−{tilde over (w)}k(Qk+Ak−1)|Qk] (37)
Furthermore, {tilde over (W)}k(Qk)=NF{tilde over (w)}k(Qk).
As proof of Lemma 4, it follows
where {tilde over (W)}k(Qk)[Wk(χk)|Qk] and
Δ{tilde over (W)}k(Qk)=[{tilde over (W)}k(Qk+Ak)−{tilde over (W)}k(Qk+Ak−1)|Qk]. Then, it follows that Thus, we can derive
Therefore, from Eqn. 38, Eqn. 34 can be obtained.
Based on the per-user per-subband Q-factor {qk(Q,|H|,s)}, the closed-form power allocation actions minimizing the R.H.S. of the per-user subband allocation Q-factor fixed point equation in Eqn. 17 can be obtained, which can be summarized in the following lemma:
Lemma 5, decentralized power control actions, given subband allocation actions sk, the optimal power control actions of user k under the linear approximation on subband allocation Q-factor in Eqn. 16 can be given by
As proof of Lemma 5, the conditional transition probability of user k is given by Pr[χkj|χki,sk,pk]=Pr[Hkj]Pr[Qkj|χki,sk, pk],
where Pr[Qkj|χkisk,pk]=
where (a) is due to Eqn. 17 and the above per-user transition probability, (b) is due to the definition {tilde over (W)}k(Qk)[Wk(χk)|Qk] and (d) is due to the definition Δ{tilde over (W)}k(Qk)=[{tilde over (W)}k(Qk+Ak)−{tilde over (W)}k(Qk+Ak−1)|Qk]. By applying standard convex optimization techniques and Lemma 4 (Δ{tilde over (W)}k(Qk)=NFδ{tilde over (w)}k(Qk)), the optimal solution to Eqn. 40 is given by Eqn. 39.
It can be noted that in a multi-level water-filling structure of the power control action, the power control action in Eqn. 39 of Lemma 5 is both function of the CSI and QSI (where it can depend on the QSI indirectly via δ{tilde over (w)}k(Qk), which can be function of {qk(Q,|H|, s)}). Moreover, according to a non-limiting aspect, it can have the form of a multi-level water-filling structure where the power is allocated according to the CSI across subbands with the water level adaptive to the QSI as previously described.
For example, applying a per-stage subband auction as described above to the system dynamics setup as described herein, a low computational complexity and signaling overhead can be obtained. Scalarized per-subband auction (∀nε{1,NF}) as illustrated in
Bidding: For the n-th subband, each user can submit a bid
Subband Allocation: The BS 102 can assign the n-th subband according to the highest bid:
where kn*=arg maxkXk,n can denote the user with the highest bid and then broadcasts the allocation results to K users 104.
Power Allocation: Each user can determine the transmit power according to:
It should be noted that, in a comparison to brute-force (CSI, QSI)-feedback schemes, each mobile station (MS) or user k would feedback CSI|Hk,n|(∀n), QSI Qk and the LM, γk. In addition, BS 102 would solve the subband allocation sk,n* and power allocation pk,n*, and would broadcast the (real number) power allocation pk,n* to the MSs or users 104. Note that for the signaling from MS or user to BS 102, quantization bits used in signaling for the bid Xk,n versus those for the CSI|Hk,n| can be expected to be similar. However, a per-subband auction as described herein is not necessarily required to feedback QSI and LM. For the signaling from BS 102 to MS or user, the per-stage auction as described herein can employ 1 bit per subband for sk,n*, according to a non-limiting aspect. However, brute-force (CSI,QSI)-feedback schemes can require substantially more bits per subband for a relatively accurate pk,n* to ensure acceptable performance. Therefore, compared with the brute-force (CSI,QSI)-feedback schemes for uplink OFDMA systems (e.g., uplink OFDMA systems 100, etc.), a scalarized per-subband auction can advantageously reduce signaling overhead and computation complexity (at the BS 102) for subband allocation and power allocation in a decentralized solution.
According to further non-limiting implementations, an online per-user primal-dual learning algorithm via stochastic approximation can be employed, as described above, to estimate {qk(Q,|H|,s)} and LMs. For instance, the update equations for LMs can be the same as Eqns. 21 and 22, and thus, the online learning of per-user per-subband Q-factor {qk(Q,|H|,s)} can be described as follows, according to various non-limiting aspects. For notation convenience, the per-user per-subband state-action pair can be denoted as φ(Q,|H|,s). Let i (1≦i≦Iφ) be a dummy index enumerating over all the possible state-action pairs of each user over one subband with cardinality Iφ=2NH(NQ+1) and φk,n(t)(Qk(t),|Hk,n(t)|,sk,n(t)) be the current state-action pair observed at MS k on subband n at the t-th slot. Based on the current observation φk,n(t), user k 122 can update its estimate on the per-user per-subband Q-factor according to:
q
t+1
k(φi)=qtk(φi)+εl
where
can denote the number of updates of qk(φi) until t, nikε{n:φk,n(t)=φi},
For the rate of convergence and asymptotic performance it should be noted how the convergence speed scales with the number of MS or users K 104 and the number of subbands N 106. For instance, in the asynchronous per-user per-subband Q-factor learning algorithm, at slot t, each user k 122 can update the Q-factor of all the per-user per-subband state-action pairs observed in N subbands 106. Thus, the convergence speed of the asynchronous per-user per-subband Q-factor learning algorithm can depend on the speed that every per-user per-subband state-action pair of each user k is visited at the steady state. Thus, the ergodic visiting speed for each MS or user 104k 122 can be defined as
where
can denote the number of updates of qk(φi) up to slot t. The following lemma summarizes various non-limiting aspects regarding the ergodic visiting speed.
Lemma 6, ergodic visiting speed with respect to K and N, the ergodic visiting speed for each MS or user 104 k 122 of the per-user per-subband Q-factor stochastic learning algorithm in Eqn. 43 can be given by Vk=(N/K)(∀k).
As proof of Lemma 6, K can be fixed such that the growth can be considered of the ergodic visiting speed with respect to N. As N increases, the number of per-user per-subband state-action pair observations made at each time slot increases (this “parallelism” helps to speed up the convergence rate). Thus, the chance that all per-user per-subband state-action pair of each user is visited grows like (N), and hence, the ergodic visiting speed of each user grows like (N). Next, N can be fixed and consider the growth of the ergodic visiting speed with respect to K. Each subband can only be allocated to one user. Thus, the chance of the bottleneck state-action pair with s=1 for each user being visited decreases like (K), and hence, the ergodic visiting speed of each user grows like (1/K). Combining the above two cases, Lemma 6 can be shown.
It is noted that the convergence rate of the learning algorithm is related to Vk=(N/K). Observe that the convergence speed increases as N increases. This is because in the asynchronous update process in Eqn. 43, each user k updates the Q-factor of all the per-user per-subband state-action pair observed in N subbands in a single time slot. Thus, it can be understood that there can advantageously be intrinsic parallelism in the learning process across different subbands.
In addition, for various non-limiting implementations, it can be shown that the performance of the distributed algorithm is asymptotically global optimal for large number of users.
Theorem 2, asymptotically global optimal, for sufficiently large K 104 such that the optimization Problem 1 can be feasible, the performance of the online distributed per-user primal-dual learning algorithm can be expected to be asymptotically global optimal, e.g.,
and γ∞→γ* as K→∞, where *(χ,s) and γ* can denote the solution of the centralized Bellman equation in Eqn. 13 satisfying the corresponding constraints in Eqns. 9 and 10.
As proof of theorem 2, for given γ, it can be proven that under a Best-CSI subband allocation policy, the Q-factor satisfying the Bellman equation in Eqn. 13 can be decomposed into the additive form in Eqn. 15. Based on that, it can be shown that for large K, the linear Q-factor approximation in Eqn. 16 can indeed be optimal.
Definition 2, best-CSI subband allocation policy, a best-CSI subband allocation policy can be defined as
where
{tilde over (s)}
k,n(Hn)=1[|Hk,n|=maxj|Hj,n|]=1[|Hk,n|≧maxj≠k|Hj,n|] (44)
A property can first be established of the Q-factor in the original Bellman equation in Eqn. 13 under the Best-CSI subband allocation policy, which can be summarized in Lemma 7.
Lemma 7, additive property of the subband allocation Q-factor, under a Best-CSI subband allocation policy, the solution to the original Bellman equation in Eqn. 13 can be expressed into the form
where {∞k(χk,sk)} can denote the converged per-user Q-factor, which can also be the solution of the k-th user's per-user subband allocation Q-factor fixed point equation given by Eqn. 17.
Under the Best-CSI subband allocation policy, the Bellman equation in Eqn. 13 becomes
where (a) is due to Eqn. 7 and the definition {tilde over (V)}(Q)(χ,{tilde over (Ω)}s(H))|Q], (b) can be obtained by taking conditional expectation (conditioned on Qi) on both sides of Eqn. 45 and the definition of {tilde over (V)}(Q). In addition, denote
Δk{tilde over (V)}(Q)[{tilde over (V)}(Q+A)−{tilde over (V)}(Q+A−ek)|Q].
From Eqn. 45, it can be shown that {(χi,s)} can be determined by {{tilde over (V)}(Qi)}. Next, solving {{tilde over (V)}(Qi)} by the IQ equations in Eqn. 46, first, assume the linear approximation
holds under the best-CSI subband allocation policy, it follows that
Thus, the optimal power allocation and corresponding conditional departure rate to minΩ
Therefore, from Eqn. 46, it follows that
{tilde over (g)}
k(γk,Qki)
where
{tilde over (μ)}k(Qk)=[μk(Qk,Hk,{tilde over (s)}k(H))|Qk]. Since there can be (NQ+1) QSI states for each user and the structure in Eqn. 49 can be decoupled under the additive assumption, for each user k, there are only (NQ+1) independent Poisson equations with NQ+2 unknowns {θk,{tilde over (W)}k(Qk)}. θk can be unique and {{tilde over (W)}k(Qk)} can be unique up to an additive constant. Therefore, {θ,{tilde over (V)}(Q)} can be the solution to Eqn. 46, where
and
Next, it can be shown that
and
into Eqn. 45, it follows that
where
which can be equivalent to Eqn. 17. By Lemma 2, the converged {∞k(χk,sk)} can satisfy Eqn. 16, which can complete the proof
Next, the asymptotic subband allocation results for large K can be considered. The optimal control actions to Eqn. 13 are given by
where {tilde over (V)}*(Q)[mins*(χ,s)|Q], Δk{tilde over (V)}*(Q)[{tilde over (V)}*(Q+A)−[{tilde over (V)}*(Q+A−ek)|Q]and
Denote kn*arg maxk|Hk,n|2. For large K, |Hk,n|2 grows with log(K) by extreme value theory. Because the traffic loading remains unchanged as it is scale up K, maxk,j|Δk{tilde over (V)}*(Q)−Δj{tilde over (V)}*(Q)|=O(1). Hence, Xk*
In view of the exemplary embodiments described supra, methods that can be implemented in accordance with the disclosed subject matter will be better appreciated with reference to the flowcharts of
At 406, methods 400 can include updating the set of parameters of the one or more mobile stations 104 based on auction results from the per-stage subband auction. For instance, as describe herein regarding online policy improvement, at the beginning of the t-th slot, BS 102 can perform the per-stage subband auction to obtain policy Ωt=(Ωp,Ωs) for the t-th slot. In a further example regarding online potential and LM updating as described herein, at the end of the t-th slot, each mobile station 104 or user k=1:K can update the potential per-user per-subband subband allocation Q-factor, qt+1k according to Eqn. 25 and can update the Lagrange multiplier γt+1k according to Eqns. 26 and 31 for the t+1-th slot. In addition, methods 400 can further include determining a transmit power based on the subband allocation result, as further described herein.
Thus, at 408 it can be determined whether the set of parameters meet acceptance criteria, For example, according to a non-limiting aspect as further described above, a policy Ω can be called feasible if the associated actions (e.g., subband and power allocation) can satisfy an average total transmit power constraint and a subband assignment constraint (e.g., satisfies the power and packet drop rate constraints in Eqns. 9 and 10). In a further non-limiting example, as described below regarding
In addition, at 504, methods 500 for resource allocation can also comprise receiving bids for resource allocation from one or more mobile stations. As a non-limiting example, methods 500 can include receiving bids for resource allocation (e.g., subband allocation according to a subband allocation policy, etc.) from one or more mobile stations 104 (e.g., users, mobile users, mobile devices, mobile stations, etc.). For instance, as further described herein, each mobile station 104 can submit one or more bid(s) to the base station. As a further non-limiting example, based on the local observation χk, each user k 122 can submit a bid {k(χk,sk):∀sk} to BS 102.
In addition, methods 500 can include generating (e.g., a generating via a processor, and so on, as further described herein regarding,
Moreover, at 508, methods 500 can further include assigning a subband, based on the resource allocation policy, to one or more mobile stations 104 for the current slot. In a non-limiting example, methods 500 can further include broadcasting subband allocation results of the auction mechanism to the plurality of mobile stations. For instance, as described above regarding subband allocation, BS 102 can assign the n-th subband according to the highest bid as per Eqn. 24 and can then broadcasts the allocation results to K users 104, where sk,n, pk,n can denote subband and power allocation action, respectively, for user k=1:K. As a result, each mobile station 104 can receive the subband allocation results and can perform power allocation, as further described herein.
Thus, at 510, methods 500 can include receiving a transmission from one or more mobile stations 104 that can employ a transmit power determined by the one or more mobile stations based on the subband allocation results. As a further non-limiting example, as described above, regarding power allocation, each user or mobile station 104 can determine transmit power pk,n according to Eqn. 25 for user k=1:K. Thus, as describe above regarding
In view of the methods described supra, systems and devices that can be implemented in accordance with the disclosed subject matter will be better appreciated with reference to the functional block diagrams of
In addition, as mentioned, BS 102 can comprise, employ, or be associated with a cross-layer controller 116 (e.g., a resource allocation controller, a resource allocation controller component (RACC), etc). Thus, in further non-limiting implementations of system 600, a resource allocation controller component 116 can be associated with the BS 102. In a non-limiting aspect, resource allocation controller component 116 can be configured to determine joint QSI as a function of the local QSI, as further described herein.
In addition, resource allocation controller component 116 can comprise, employ, or be associated with a subband auction component 602. For instance, systems 600 can comprise a subband auction component 602 associated with the resource allocation controller component 116. In a further non-limiting aspect, subband auction component 602 can be configured to perform a per-stage subband auction, based on the local CSI and the joint QSI. Moreover, in further non-limiting implementations, subband auction component 602 can be further configured to determine a resource allocation policy that can includes one or more of a power allocation policy and a subband allocation policy for the mobile stations 104. Additionally, in other non-limiting implementations, resource allocation controller component 116 can also be configured to determine whether an average power constraint or a packet drop constraint is satisfied for the resource allocation policy, as further described above, for example, regarding
In yet other non-limiting implementations, systems 600 can further comprise a subband allocation component 604. For example, systems 600 can further comprise a subband allocation component 604 associated with the resource allocation controller component 116. In an exemplary aspect, subband allocation component 604 can be configured to assign a subband to one or more mobile stations, according to subband allocation results of the per-stage subband auction, as further described herein (e.g., the per-stage subband auction assigns subbands based on bids for resource allocation from the plurality of mobile stations, etc.). In a further non-limiting example, subband allocation component 604 can be further configured to broadcast the subband allocation results to one or more mobile stations. Further discussion of the advantages and flexibility provided by the various non-limiting embodiments can be appreciated by review of the following description.
For example,
Memory 702 can further include instructions pertaining to receiving a transmission from the mobile station employing a transmit power determined by the mobile station based on the subband allocation results; to approximating the joint QSI as a function of a set of local QSI associated with individual mobile stations of the one or more mobile stations; to determining whether the average power constraint and the packet drop constraint are satisfied for the resource allocation policy; to determining the resource allocation policy based on observing joint CSI and joint QSI associated with the one or more mobile stations; to determining a subband allocation policy including the subband allocation results and a transmit power policy for the one or more mobile stations; to simultaneously updating LM, based on an average power constraint and a packet drop constraint, and one of the set of local QSI associated with individual mobile stations; and/or to broadcasting subband allocation results of the per-stage subband auction mechanism to the one or more mobile stations. The above example instructions and other suitable instructions can be retained within memory 702, and a processor 704 can be utilized in connection with executing the instructions.
In further non-limiting implementations, resource allocation controller 116 can comprise processor 704, and/or computer readable instructions stored on a non-transitory computer readable storage medium (e.g., memory 702, a hard disk drive, and so on, etc.), the computer readable instructions, when executed by a computing device, e.g., processor 704, can cause the computing device perform operations, according to various aspects of the disclosed subject matter. For instance, as a non-limiting example, the computer readable instructions, when executed by a computing device, can cause the computing device generate a resource allocation policy, based on bids for resource allocation from one or more mobile stations and a per-stage subband auction mechanism for a current slot, assign a subband, based on the resource allocation policy, to a mobile station of the one or more mobile stations for the current slot, and so on, etc., as described herein.
Accordingly, in further non-limiting embodiments, the disclosed subject matter provides a computer readable storage medium (e.g., a hard disk drive, optical drive, a memory, a flash memory, and so on, etc.) comprising computer executable instructions that, in response to execution, cause a computing device to perform operations as described herein. For instance, computer executable instructions can cause a computing device, to perform operations such as, receiving bids for resource allocation from one or more mobile devices, generating a resource allocation policy for a current schedule slot of one or more schedule slots including auctioning subbands based on the bids, and assigning a subband, based on the resource allocation policy, to a mobile device of the one or more mobile devices for the current slot, as well as other operations as described above regarding
Processor 806 can be a processor dedicated to analyzing information received by input component 802 and/or generating information for transmission by an output component 818. Processor 806 can be a processor that controls one or more portions of systems or apparatuses 800, and/or a processor that can analyze information received by input component 802, can generate information for transmission by output component 818, and can perform various power and subband allocation algorithms associated with RACC 116, or as further described herein. In addition, systems or apparatuses 800 can further include a RACC 116, as described above and that can perform various techniques as described herein, in addition to the various other functions required by other components as described above.
While RACC 116 is shown external to the processor 806 and memory 810, it is to be appreciated that RACC 116 can include code or instructions stored in storage component 804 and subsequently retained in memory 810 for execution by processor 806. In addition, RACC 116 can utilize artificial intelligence based methods in connection with performing inference and/or probabilistic determinations and/or statistical-based determinations in connection applying the power and subband allocation techniques described herein.
Systems or apparatuses 800 can additionally comprise memory 810 that is operatively coupled to processor 806 and that stores information such as described above, parameters, information, and the like, wherein such information can be employed in connection with implementing the power and subband allocation techniques as described herein. Memory 810 can additionally store protocols associated with generating lookup tables, etc., such that systems or apparatuses 800 can employ stored protocols and/or algorithms further to the performance of various algorithms and/or portions thereof as described herein.
It will be appreciated that storage component 804 and memory 806, or any combination thereof as described herein, can be either volatile memory or nonvolatile memory, or can include both volatile and nonvolatile memory. By way of illustration, and not limitation, nonvolatile memory can include read only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM), which acts as cache memory. By way of illustration and not limitation, RAM is available in many forms such as synchronous RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), Synch link DRAM (SLDRAM), and direct Rambus RAM (DRRAM). The memory 810 is intended to comprise, without being limited to, these and any other suitable types of memory, including processor registers and the like. In addition, by way of illustration and not limitation, storage component 804 can include conventional storage media as in known in the art (e.g., hard disk drive).
Accordingly, in further non-limiting implementations, exemplary systems or apparatuses 800, such as a resource allocation controller 116 in a wireless communication system, can comprise means for performing a per-stage subband auction, on behalf of one or more mobile users, for a current schedule slot of one or more schedule slots. For instance, RACC 116 can comprise means for receiving bids for resource allocation from the one or more mobile users, as further described herein. Furthermore, RACC 116 can comprise a means for generating a resource allocation policy based the per-stage subband auction, for example, as described above regarding
In addition, exemplary RACC 116 can further comprise means for assigning a subband, based on the resource allocation policy, to a mobile user of the one or more mobile users, for example, as described above regarding
In further non-limiting embodiments of exemplary systems or apparatuses 800, RACC 116 can also include means for observing joint CSI and joint QSI associated with the one or more mobile users, and means for approximating the joint QSI as a function of a set of local QSI associated with individual mobile users of the one or more mobile users, as described above regarding
It can be understood that in various non-limiting implementations, various aspects of the disclosed subject matter can be performed by a mobile device 104 (e.g., one or more users, mobile users, mobile devices, mobile stations, etc.). That is, various non-limiting aspects of the disclosed subject matter can be performed by a mobile device 104 having portions of
Referring again to
In addition, it can be assumed that there are 64 subbands with total bandwidth (BW) of 10 MegaHertz (MHz), and the number of independent subbands NF 106 can be 4. The scheduling slot duration τ is chosen as 5 ms, and the buffer size NQ is chosen as 10.
Thus,
It can be understood that while a brief overview of exemplary systems, methods, scenarios, and/or devices has been provided, the disclosed subject matter is not so limited. Thus, it can be further understood that various modifications, alterations, addition, and/or deletions can be made without departing from the scope of the embodiments as described herein. Accordingly, similar non-limiting implementations can be used or modifications and additions can be made to the described embodiments for performing the same or equivalent function of the corresponding embodiments without deviating therefrom.
Exemplary Computer Networks and Environments
One of ordinary skill in the art can appreciate that the disclosed subject matter can be implemented in connection with any computer or other client or server device, which can be deployed as part of a communications system, a computer network, or in a distributed computing environment, connected to any kind of data store. In this regard, the disclosed subject matter pertains to any computer system or environment having any number of memory or storage units, and any number of applications and processes occurring across any number of storage units or volumes, which may be used in connection with communication systems using the scheduling techniques, systems, and methods in accordance with the disclosed subject matter. The disclosed subject matter may apply to an environment with server computers and client computers deployed in a network environment or a distributed computing environment, having remote or local storage. The disclosed subject matter may also be applied to standalone computing devices, having programming language functionality, interpretation and execution capabilities for generating, receiving and transmitting information in connection with remote or local services and processes.
Distributed computing provides sharing of computer resources and services by exchange between computing devices and systems. These resources and services include the exchange of information, cache storage, and disk storage for objects, such as files. Distributed computing takes advantage of network connectivity, allowing clients to leverage their collective power to benefit the entire enterprise. In this regard, a variety of devices may have applications, objects, or resources that may implicate the communication systems using the scheduling techniques, systems, and methods of the disclosed subject matter.
It can also be appreciated that an object, such as 1420c, may be hosted on another computing device 1410a, 1410b, etc. or 1420a, 1420b, 1420c, 1420d, 1420e, etc. Thus, although the physical environment depicted may show the connected devices as computers, such illustration is merely exemplary and the physical environment may alternatively be depicted or described comprising various digital devices such as PDAs, televisions, MP3 players, etc., any of which may employ a variety of wired and wireless services, software objects such as interfaces, COM objects, and the like.
There is a variety of systems, components, and network configurations that support distributed computing environments. For example, computing systems may be connected together by wired or wireless systems, by local networks or widely distributed networks. Currently, many of the networks are coupled to the Internet, which provides an infrastructure for widely distributed computing and encompasses many different networks. Any of the infrastructures may be used for communicating information used in the communication systems using the scheduling techniques, systems, and methods according to the disclosed subject matter.
The Internet commonly refers to the collection of networks and gateways that utilize the Transmission Control Protocol/Internet Protocol (TCP/IP) suite of protocols, which are well known in the art of computer networking. The Internet can be described as a system of geographically distributed remote computer networks interconnected by computers executing networking protocols that allow users to interact and share information over network(s). Because of such widespread information sharing, remote networks such as the Internet have thus far generally evolved into an open system with which developers can design software applications for performing specialized operations or services, essentially without restriction.
Thus, the network infrastructure enables a host of network topologies such as client/server, peer-to-peer, or hybrid architectures. The “client” is a member of a class or group that uses the services of another class or group to which it is not related. Thus, in computing, a client is a process, e.g., roughly a set of instructions or tasks, that requests a service provided by another program. The client process utilizes the requested service without having to “know” any working details about the other program or the service itself. In client/server architecture, particularly a networked system, a client is usually a computer that accesses shared network resources provided by another computer, e.g., a server. In the illustration of
A server is typically a remote computer system accessible over a remote or local network, such as the Internet or wireless network infrastructures. The client process may be active in a first computer system, and the server process may be active in a second computer system, communicating with one another over a communications medium, thus providing distributed functionality and allowing multiple clients to take advantage of the information-gathering capabilities of the server. Any software objects utilized pursuant to communication (wired or wirelessly) using the scheduling techniques, systems, and methods of the disclosed subject matter may be distributed across multiple computing devices or objects.
Client(s) and server(s) communicate with one another utilizing the functionality provided by protocol layer(s). For example, HyperText Transfer Protocol (HTTP) is a common protocol that is used in conjunction with the World Wide Web (WWW), or “the Web.” Typically, a computer network address such as an Internet Protocol (IP) address or other reference such as a Universal Resource Locator (URL) can be used to identify the server or client computers to each other. The network address can be referred to as a URL address. Communication can be provided over a communications medium, e.g., client(s) and server(s) may be coupled to one another via TCP/IP connection(s) for high-capacity communication.
Thus,
In a network environment in which the communications network/bus 1440 is the Internet, for example, the servers 1410a, 1410b, etc. can be Web servers with which the clients 1420a, 1420b, 1420c, 1420d, 1420e, etc. communicate via any of a number of known protocols such as HTTP. Servers 1410a, 1410b, etc. may also serve as clients 1420a, 1420b, 1420c, 1420d, 1420e, etc., as may be characteristic of a distributed computing environment.
As mentioned, communications to or from the systems incorporating the scheduling techniques, systems, and methods of the disclosed subject matter may ultimately pass through various media, either wired or wireless, or a combination, where appropriate. Client devices 1420a, 1420b, 1420c, 1420d, 1420e, etc. may or may not communicate via communications network/bus 14, and may have independent communications associated therewith. For example, in the case of a TV or VCR, there may or may not be a networked aspect to the control thereof. Each client computer 1420a, 1420b, 1420c, 1420d, 1420e, etc. and server computer 1410a, 1410b, etc. may be equipped with various application program modules or objects 1435a, 1435b, 1435c, etc. and with connections or access to various types of storage elements or objects, across which files or data streams may be stored or to which portion(s) of files or data streams may be downloaded, transmitted or migrated. Any one or more of computers 1410a, 1410b, 1420a, 1420b, 1420c, 1420d, 1420e, etc. may be responsible for the maintenance and updating of a database 1430 or other storage element, such as a database or memory 1430 for storing data processed or saved based on communications made according to the disclosed subject matter. Thus, the disclosed subject matter can be utilized in a computer network environment having client computers 1420a, 1420b, 1420c, 1420d, 1420e, etc. that can access and interact with a computer network/bus 1440 and server computers 1410a, 1410b, etc. that may interact with client computers 1420a, 1420b, 1420c, 1420d, 1420e, etc. and other like devices, and databases 1430.
As mentioned, the disclosed subject matter applies to any device wherein it may be desirable to communicate data, e.g., to or from a mobile device. It should be understood, therefore, that handheld, portable and other computing devices and computing objects of all kinds are contemplated for use in connection with the disclosed subject matter, e.g., anywhere that a device may communicate data or otherwise receive, process or store data. Accordingly, the below general purpose remote computer described below in
Although not required, the some aspects of the disclosed subject matter can partly be implemented via an operating system, for use by a developer of services for a device or object, and/or included within application software that operates in connection with the component(s) of the disclosed subject matter. Software may be described in the general context of computer executable instructions, such as program modules, being executed by one or more computers, such as client workstations, servers or other devices. Those skilled in the art will appreciate that the disclosed subject matter may be practiced with other computer system configurations and protocols.
With reference to
Computer 1510a typically includes a variety of computer readable media. Computer readable media can be any available media that can be accessed by computer 1510a. By way of example, and not limitation, computer readable media may comprise computer storage media and communication media. Computer storage media includes volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data. Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CDROM, digital versatile disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can be accessed by computer 1510a. Communication media typically embodies computer readable instructions, data structures, program modules, or other data in a modulated data signal such as a carrier wave or other transport mechanism and includes any information delivery media.
The system memory 1530a may include computer storage media in the form of volatile and/or nonvolatile memory such as read only memory (ROM) and/or random access memory (RAM). A basic input/output system (BIOS), containing the basic routines that help to transfer information between elements within computer 1510a, such as during start-up, may be stored in memory 1530a. Memory 1530a typically also contains data and/or program modules that are immediately accessible to and/or presently being operated on by processing unit 1520a. By way of example, and not limitation, memory 1530a may also include an operating system, application programs, other program modules, and program data.
The computer 1510a may also include other removable/non-removable, volatile/nonvolatile computer storage media. For example, computer 1510a could include a hard disk drive that reads from or writes to non-removable, nonvolatile magnetic media, a magnetic disk drive that reads from or writes to a removable, nonvolatile magnetic disk, and/or an optical disk drive that reads from or writes to a removable, nonvolatile optical disk, such as a CD-ROM or other optical media. Other removable/non-removable, volatile/nonvolatile computer storage media that can be used in the exemplary operating environment include, but are not limited to, magnetic tape cassettes, flash memory cards, digital versatile disks, digital video tape, solid state RAM, solid state ROM, and the like. A hard disk drive is typically connected to the system bus 1521a through a non-removable memory interface such as an interface, and a magnetic disk drive or optical disk drive is typically connected to the system bus 1521a by a removable memory interface, such as an interface.
A user may enter commands and information into the computer 1510a through input devices such as a keyboard and pointing device, commonly referred to as a mouse, trackball, or touch pad. Other input devices may include a microphone, joystick, game pad, satellite dish, scanner, wireless device keypad, voice commands, or the like. These and other input devices are often connected to the processing unit 1520a through user input 1540a and associated interface(s) that are coupled to the system bus 1521a, but may be connected by other interface and bus structures, such as a parallel port, game port or a universal serial bus (USB). A graphics subsystem may also be connected to the system bus 1521a. A monitor or other type of display device is also connected to the system bus 1521a via an interface, such as output interface 1550a, which may in turn communicate with video memory. In addition to a monitor, computers may also include other peripheral output devices such as speakers and a printer, which may be connected through output interface 1550a.
The computer 1510a may operate in a networked or distributed environment using logical connections to one or more other remote computers, such as remote computer 1570a, which may in turn have media capabilities different from device 1510a. The remote computer 1570a may be a personal computer, a server, a router, a network PC, a peer device, personal digital assistant (PDA), cell phone, handheld computing device, or other common network node, or any other remote media consumption or transmission device, and may include any or all of the elements described above relative to the computer 1510a. The logical connections depicted in
When used in a LAN networking environment, the computer 1510a is connected to the LAN 1571a through a network interface or adapter. When used in a WAN networking environment, the computer 1510a typically includes a communications component, such as a modem, or other means for establishing communications over the WAN, such as the Internet. A communications component, such as a modem, which may be internal or external, may be connected to the system bus 1521a via the user input interface of input 1540a, or other appropriate mechanism. In a networked environment, program modules depicted relative to the computer 1510a, or portions thereof, may be stored in a remote memory storage device. It will be appreciated that the network connections shown and described are exemplary and other means of establishing a communications link between the computers may be used.
While the disclosed subject matter has been described in connection with the preferred embodiments of the various figures, it is to be understood that other similar embodiments may be used or modifications and additions may be made to the described embodiment for performing the same function of the disclosed subject matter without deviating therefrom. For example, one skilled in the art will recognize that the disclosed subject matter as described in the present application applies to communication systems using the disclosed scheduling techniques, systems, and methods and may be applied to any number of devices connected via a communications network and interacting across the network, either wired, wirelessly, or a combination thereof.
Accordingly, while words such as transmitted and received are used in reference to the described communications processes, it should be understood that such transmitting and receiving is not limited to digital communications systems, but could encompass any manner of sending and receiving data suitable for implementation of the described scheduling techniques. As a result, the disclosed subject matter should not be limited to any single embodiment, but rather should be construed in breadth and scope in accordance with the appended claims.
Exemplary Communications Networks and Environments
The above-described communication systems using the scheduling techniques, systems, and methods may be applied to any network, however, the following description sets forth some exemplary telephony radio networks and non-limiting operating environments for communications made incident to the communication systems using the scheduling techniques, systems, and methods of the disclosed subject matter. The below-described operating environments should be considered non-exhaustive, however, and thus, the below-described network architecture merely shows one network architecture into which the disclosed subject matter may be incorporated. One can appreciate, however, that the disclosed subject matter may be incorporated into any now existing or future alternative architecture for communication networks as well.
The global system for mobile communication (“GSM”) is one of the most widely utilized wireless access systems in today's fast growing communication systems. GSM provides circuit-switched data services to subscribers, such as mobile telephone or computer users. General Packet Radio Service (“GPRS”), which is an extension to GSM technology, introduces packet switching to GSM networks. GPRS uses a packet-based wireless communication technology to transfer high and low speed data and signaling in an efficient manner GPRS optimizes the use of network and radio resources, thus enabling the cost effective and efficient use of GSM network resources for packet mode applications.
As one of ordinary skill in the art can appreciate, the exemplary GSM/GPRS environment and services described herein can also be extended to 3G services, such as Universal Mobile Telephone System (“UMTS”), Frequency Division Duplexing (“FDD”) and Time Division Duplexing (“TDD”), High Speed Packet Data Access (“HSPDA”), cdma2000 1x Evolution Data Optimized (“EVDO”), Code Division Multiple Access-2000 (“cdma2000 3x”), Time Division Synchronous Code Division Multiple Access (“TD-SCDMA”), Wideband Code Division Multiple Access (“WCDMA”), Enhanced Data GSM Environment (“EDGE”), International Mobile Telecommunications-2000 (“IMT-2000”), Digital Enhanced Cordless Telecommunications (“DECT”), etc., as well as to other network services that shall become available in time. In this regard, the scheduling techniques, systems, and methods of the disclosed subject matter may be applied independently of the method of data transport, and does not depend on any particular network architecture, or underlying protocols.
Generally, there can be four different cell sizes in a GSM network-macro, micro, pico and umbrella cells. The coverage area of each cell is different in different environments. Macro cells can be regarded as cells where the base station antenna is installed in a mast or a building above average roof top level. Micro cells are cells whose antenna height is under average roof top level; they are typically used in urban areas. Pico cells are small cells having a diameter is a few dozen meters; they are mainly used indoors. On the other hand, umbrella cells are used to cover shadowed regions of smaller cells and fill in gaps in coverage between those cells.
The word “exemplary” is used herein to mean serving as an example, instance, or illustration. For the avoidance of doubt, the subject matter disclosed herein is not limited by such examples. In addition, any aspect or design described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other aspects or designs, nor is it meant to preclude equivalent exemplary structures and techniques known to those of ordinary skill in the art. Furthermore, to the extent that the terms “includes,” “has,” “contains,” and other similar words are used in either the detailed description or the claims, for the avoidance of doubt, such terms are intended to be inclusive in a manner similar to the term “comprising” as an open transition word without precluding any additional or other elements.
Various implementations of the disclosed subject matter described herein may have aspects that are wholly in hardware, partly in hardware and partly in software, as well as in software. Furthermore, aspects may be fully integrated into a single component, be assembled from discrete devices, or implemented as a combination suitable to the particular application and is a matter of design choice. As used herein, the terms “node,” “terminal,” “access point,” “base station,” “component,” “system,” and the like are likewise intended to refer to a computer-related entity, either hardware, a combination of hardware and software, software, or software in execution. For example, a component may be, but is not limited to being, a process running on a processor, a processor, an object, an executable, a thread of execution, a program, and/or a computer. By way of illustration, both an application running on computer and the computer can be a component. One or more components may reside within a process and/or thread of execution and a component may be localized on one computer and/or distributed between two or more computers.
Thus, the systems of the disclosed subject matter, or certain aspects or portions thereof, may take the form of program code (e.g., instructions) embodied in tangible media, such as floppy diskettes, CD-ROMs, hard drives, or any other machine-readable storage medium, wherein, when the program code is loaded into and executed by a machine, such as a computer, the machine becomes an apparatus for practicing the disclosed subject matter. In the case of program code execution on programmable computers, the computing device generally includes a processor, a storage medium readable by the processor (including volatile and non-volatile memory and/or storage elements), at least one input device, and at least one output device. In addition, the components may communicate via local and/or remote processes such as in accordance with a signal having one or more data packets (e.g., data from one component interacting with another component in a local system, distributed system, and/or across a network such as the Internet with other systems via the signal).
As used in this application, the term “or” is intended to mean an inclusive “or” rather than an exclusive “or”. That is, unless specified otherwise, or clear from context, “X employs A or B” is intended to mean any of the natural inclusive permutations. That is, if X employs A; X employs B; or X employs both A and B, then “X employs A or B” is satisfied under any of the foregoing instances. In addition, the articles “a” and “an” as used in this application and the appended claims should generally be construed to mean “one or more” unless specified otherwise or clear from context to be directed to a singular form.
As used herein, the terms to “infer” or “inference” refer generally to the process of reasoning about or inferring states of the system, environment, and/or user from a set of observations as captured via events and/or data. Inference can be employed to identify a specific context or action, or can generate a probability distribution over states, for example. The inference can be probabilistic—that is, the computation of a probability distribution over states of interest based on a consideration of data and events. Inference can also refer to techniques employed for composing higher-level events from a set of events and/or data. Such inference results in the construction of new events or actions from a set of observed events and/or stored event data, whether or not the events are correlated in close temporal proximity, and whether the events and data come from one or several event and data sources.
Furthermore, the some aspects of the disclosed subject matter may be implemented as a system, method, apparatus, or article of manufacture using standard programming and/or engineering techniques to produce software, firmware, hardware, or any combination thereof to control a computer or processor based device to implement aspects detailed herein. The terms “article of manufacture”, “computer program product” or similar terms, where used herein, are intended to encompass a computer program accessible from any computer-readable device, carrier, or media. For example, computer readable media can include but are not limited to magnetic storage devices (e.g., hard disk, floppy disk, magnetic strips, etc.), optical disks (e.g., compact disk (CD), digital versatile disk (DVD), etc.), smart cards, and flash memory devices (e.g., card, stick, key drive, etc.). Additionally, it is known that a carrier wave can be employed to carry computer-readable electronic data such as those used in transmitting and receiving electronic mail or in accessing a network such as the Internet or a local area network (LAN). Of course, those skilled in the art will recognize many modifications may be made to this configuration without departing from the scope or spirit of the various embodiments.
The aforementioned systems have been described with respect to interaction between several components. It can be appreciated that such systems and components can include those components or specified sub-components, some of the specified components or sub-components, and/or additional components, and according to various permutations and combinations of the foregoing. Sub-components can also be implemented as components communicatively coupled to other components rather than included within parent components, e.g., according to a hierarchical arrangement. Additionally, it should be noted that one or more components may be combined into a single component providing aggregate functionality or divided into several separate sub-components, and any one or more middle layers, such as a management layer, may be provided to communicatively couple to such sub-components in order to provide integrated functionality. Any components described herein may also interact with one or more other components not specifically described herein but generally known by those of skill in the art.
While for purposes of simplicity of explanation, methodologies disclosed herein are shown and described as a series of blocks, it is to be understood and appreciated that the claimed subject matter is not limited by the order of the blocks, as some blocks may occur in different orders and/or concurrently with other blocks from what is depicted and described herein. Where non-sequential, or branched, flow is illustrated via flowchart, it can be appreciated that various other branches, flow paths, and orders of the blocks, may be implemented which achieve the same or a similar result. Moreover, not all illustrated blocks may be required to implement the methodologies described hereinafter.
Furthermore, as will be appreciated various portions of the disclosed systems may include or consist of artificial intelligence or knowledge or rule based components, sub-components, processes, means, methodologies, or mechanisms (e.g., support vector machines, neural networks, expert systems, Bayesian belief networks, fuzzy logic, data fusion engines, classifiers . . . ). Such components, inter alia, can automate certain mechanisms or processes performed thereby to make portions of the systems and methods more adaptive as well as efficient and intelligent.
While the disclosed subject matter has been described in connection with the particular embodiments of the various figures, it is to be understood that other similar embodiments may be used or modifications and additions may be made to the described embodiment for performing the same function of the disclosed subject matter without deviating therefrom. Still further, the disclosed subject matter may be implemented in or across a plurality of processing chips or devices, and storage may similarly be effected across a plurality of devices. Therefore, the disclosed subject matter should not be limited to any single embodiment, but rather should be construed in breadth and scope in accordance with the appended claims.
This application claims priority to U.S. Provisional Patent Application No. 61/483,509, entitled DISTRIBUTIVE STOCHASTIC LEARNING FOR DELAY-OPTIMAL OFDMA POWER AND SUBBAND ALLOCATION, and filed on May 6, 2011, the entirety of which is incorporated herein by reference.
Number | Date | Country | |
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61483509 | May 2011 | US |